Is there a way in which this could be interpreted to give relativistic mass to distant objects?
No. The strong nuclear force (which is discussed here) is short ranged — it doesn't really extend past an atomic nucleus.
There is long range binding energy due to gravity, of course. That's what holds the galaxy together. But gravitational binding energy isn't dark matter; we already account for it.
It's not a meaningless statement. It's a perfectly correct statement of the limits of validity of the Newtonian approximation.
All scientific theories probably are wrong. So?
It's not correct to conclude that all theories are wrong because we can't verify them to infinite precision, though. Being unable to verify a theory doesn't mean it's wrong, it just means we can't prove it's right.
There is no frame of reference in which Newtonian mechanics is correct. How objects are moving has nothing to do with what frame of reference you choose to use. You can choose a frame which is at rest with respect to one or more objects, but you don't have to, and your choice is irrelevant to the laws of physics.
Whether E=mc^2 is valid for a non-stationary argument depends on how 'm' is defined. That symbol has been used in more than one way in the literature, although your usage is now the most common.
I gave a number of specific predictions of anthropogenic global warming which agree with observations, including the observed warming trend itself, stratospheric cooling, downward penetration of ocean heat, trends in diurnal and seasonal temperatures, etc. The predictions of all the competing natural warming theories disagree with observations for at least one and usually more than one of those tests.
In a theory of everything that tries to explain things 100% in terms of fields, there is no mass and everything is accounted for in the energy of fields generated sub-atomic particles.
Quantum field theory already explains everything in terms of fields, both fermion and boson. And there certainly is mass in QFT.
Or maybe they just forgot about another particle and another non-scalar quantum field and there is no higgs, and no missing missing mass.
It doesn't matter much to their calculation whether there's a Higgs. All that matters is that quarks have mass for some reason, and we experimentally know what that mass is. As for remaining error, I doubt it means anything. The calculation itself is only an approximation, with a numerical error of at least a few percent.
That's just interpretation. It doesn't matter how you write it: they're physically equivalent. Reordering the variables in an equation does not imply any sort of causality between them.
The equation itself is not hard to write down, but solving the equation requires a supercomputer. (Talking about the QCD results in TFA, not Schroedinger's equation.)
Most of flavors of string theory are not only falsifiable but falsified, since most string vacua don't have anything to do with the universe we observe.
People had already applied E=mc^2, that's what led them to conclude that some energy was "missing" and how much of it. The advance is that they were actually able to calculate from theory how much energy ought to be "missing", and found that it agreed with the missing amount previously inferred from E=mc^2.
This is mostly an advance in computational methods. You would apply it to a unified field theory for the same reason it was applied to QCD: the theory is so complicated that you need a supercomputer to even tell what it predicts. Once you know what it predicts, then you can test the theory against experiments.
The problem was that the math gave a formula for the mass of the proton, but the formula was so complicated nobody could actually solve it, in order to see if its prediction agrees with the proton's true mass. The advance here is to use a supercomputer to solve the formula.
You perhaps could solve it by diagonalizing gigantic matrices, but that's not what they do. The main computational effort comes from computing gigantic multidimensional integrals over millions of variables, one for each point and link in the spacetime lattice. That's what Monte Carlo methods are for; they're the only tractable way to handle very high dimensional integrals.
As noted in other posts, what is exciting about this isn't necessarily that E=mc^2 is confirmed (that's been done plenty of times before), but that it was done in a quantum world (which historically has been at odds with relativity).
What's exciting is, technically, that people were able to calculate the energy of the quark-gluon fields inside a baryon. Everyone knew what it had to be (the difference between the baryon mass and the masses of the quarks inside), but nobody had been able to calculate it directly from theory.
E=mc^2 has never been at odds with quantum field theory. It's only relativistic gravity which is at odds with quantum mechanics.
There is such a thing as relativistic mass, but most people just call it "energy" (or "mass-energy" when they're being pedantic), since as you say, you can't just blindly plug it into all the relativistic formulas where mass appears.
Nobody expected E=mc^2 to be violated. That's not why they ran the calculation. They ran the calculation because, until now, nobody has been able to calculate the mass of a proton from the masses of its constituent quarks. You could write down the formula, but it takes a supercomputer to solve it.
So in this scenario, are they then combining the two types of mass to account for 100%? The type of mass that accounts for 95% of the particle is the energy given off from gluons and quarks, which is a relativistic mass since movements and interactions don't have intrinsic mass? But the intrinsic mass of quarks makes up 5%?
Yeah, that's basically it.
Aren't they confusing various definitions of mass to explain the total mass which they think should be there?
The conserved quantity is relativistic mass. The relativistic mass of the quarks, plus the relativistic mass of the gluons, equals the relativistic mass of the proton.
This is somewhat confused by the fact that relativistic and intrinsic mass of a particle are the same at rest. So if the quarks aren't moving too much, you can basically equate their relativistic mass with their rest mass. I'm not sure which is the 5% they refer to. And then, if the proton is at rest, then the relativistic mass which all the constituents add up to becomes the proton's "intrinsic" mass, treating it as a single particle.
You're right. The "intrinsic" mass is usually called "invariant" mass or sometimes "rest mass" (although the latter doesn't apply to photons). The "relativistic mass" is called "relativistic mass", or "total mass-energy".
Take 'global warmming' both sides have a lot of theory but very little in the way of good tests that can prove it one way or the other.
You can test it by observing that natural sources of warming don't agree with the magnitude, rate, or timing of the observed warming; and that human sources do. You can further observe, for instance, that an enhanced greenhouse effect will lead to stratospheric cooling as a result of heat being trapped lower in the troposphere, and we do observe that. There are further predictions which distinguish manmade warming from various types of natural warming, depending on the type of natural warming. For instance, warming from the atmosphere means the oceans warm from the top down, which is observed, and disagrees with theories that have the surface heat come from the oceans. The greenhouse effect also means that you get shifts in the diurnal and seasonal patterns of warming which disagree with the shifts predicted by solar-induced warming, because of the daily/seasonal patterns in sunlight shifts which do not occur for the greenhouse effect. And so on.
No. They're just verifying that gluons contribute to the binding energy of baryons. A gravitational analogy: we know that the total energy of a binary star system is different from the energy of two random stars millions of light years away from each other. That's because the energy of the system is not just the mass of the stars, but the star masses plus the gravitational energy in the system. For protons, the quarks are like individual stars. We knew that the mass of the proton equals the mass of the quarks plus their binding energy (from the strong force), but until now, we weren't able to calculate that energy.
This doesn't have relevance to dark matter because dark matter can't be due to nuclear binding energy between distant particles: the nuclear force is short ranged.
It's not solving the Dirac equation (which is for a free fermion), but the full Yang-Mills equations, including the strong nuclear force. And they're not really solving DEs by finite element methods. They're evaluating functional integrals via Monte Carlo (integrating configurations over field space). But the functional to be evaluated (the action) is defined on a spacetime lattice and involves field derivatives, which is where the finite differencing comes in.
Science can't tell you whether some theoretical construct is "really" there. That's a matter of philosophical definition. All science can tell you is whether the predictions of theories agree with what is observed in the world.
Although the point of the exercise wasn't actually to verify E=mc^2, it was to develop a computer simulation capable of calculating the masses of baryons using quantum chromodynamics. You could write down a formula for them, but nobody had been able to solve it.
Most areas of science strongly rely on philosophy, and most scientists understand it poorly, usually to the detriment of the technical quality of their work.
What a foolishly over-general remark.
Fine, there are scientists who are armchair philosophers in their spare time. But the vast majority of published scientific work does not intersect with philosophy in any way that meaningfully impacts its technical quality. Hardly anyone publishes papers whose technical content involves, say, free will, or any other serious philosophical issue. If you're want to include "the scientific method", you have to provide evidence that scientists' philosophical misunderstandings of their own methods usually have a detrimental impact on their technical work. A few cherry-picked anecdotes of particularly philosophical work doesn't count.
You could try the two-volume Bamberg and Sternberg, A Course in Mathematics for Students of Physics. I think it could conversely work as a course in physics for students of mathematics. And Arnold, Mathematical Methods of Classical Mechanics. Or Nayfeh and Balachandran, Applied Nonlinear Dynamics Also Lawrie, A Unified Grand Tour of Theoretical Physics. Terse and gives you the equations up front.
If you're into differential geometry you could try The Geometry of Physics by Frankel, or Schutz's Geometrical Methods of Mathematical Physics. But that's pretty advanced physics, general relativity, gauge theory, quantum field theory and such.
Slashdot Mirror
Is there a way in which this could be interpreted to give relativistic mass to distant objects?
No. The strong nuclear force (which is discussed here) is short ranged — it doesn't really extend past an atomic nucleus.
There is long range binding energy due to gravity, of course. That's what holds the galaxy together. But gravitational binding energy isn't dark matter; we already account for it.
It's not a meaningless statement. It's a perfectly correct statement of the limits of validity of the Newtonian approximation.
All scientific theories probably are wrong. So?
It's not correct to conclude that all theories are wrong because we can't verify them to infinite precision, though. Being unable to verify a theory doesn't mean it's wrong, it just means we can't prove it's right.
There is no frame of reference in which Newtonian mechanics is correct. How objects are moving has nothing to do with what frame of reference you choose to use. You can choose a frame which is at rest with respect to one or more objects, but you don't have to, and your choice is irrelevant to the laws of physics.
Whether E=mc^2 is valid for a non-stationary argument depends on how 'm' is defined. That symbol has been used in more than one way in the literature, although your usage is now the most common.
You're not even paying attention.
I gave a number of specific predictions of anthropogenic global warming which agree with observations, including the observed warming trend itself, stratospheric cooling, downward penetration of ocean heat, trends in diurnal and seasonal temperatures, etc. The predictions of all the competing natural warming theories disagree with observations for at least one and usually more than one of those tests.
In a theory of everything that tries to explain things 100% in terms of fields, there is no mass and everything is accounted for in the energy of fields generated sub-atomic particles.
Quantum field theory already explains everything in terms of fields, both fermion and boson. And there certainly is mass in QFT.
Or maybe they just forgot about another particle and another non-scalar quantum field and there is no higgs, and no missing missing mass.
It doesn't matter much to their calculation whether there's a Higgs. All that matters is that quarks have mass for some reason, and we experimentally know what that mass is. As for remaining error, I doubt it means anything. The calculation itself is only an approximation, with a numerical error of at least a few percent.
That's just interpretation. It doesn't matter how you write it: they're physically equivalent. Reordering the variables in an equation does not imply any sort of causality between them.
The equation itself is not hard to write down, but solving the equation requires a supercomputer. (Talking about the QCD results in TFA, not Schroedinger's equation.)
Most of flavors of string theory are not only falsifiable but falsified, since most string vacua don't have anything to do with the universe we observe.
Let the pointless semantic nitpicking commence ...
People had already applied E=mc^2, that's what led them to conclude that some energy was "missing" and how much of it. The advance is that they were actually able to calculate from theory how much energy ought to be "missing", and found that it agreed with the missing amount previously inferred from E=mc^2.
This is mostly an advance in computational methods. You would apply it to a unified field theory for the same reason it was applied to QCD: the theory is so complicated that you need a supercomputer to even tell what it predicts. Once you know what it predicts, then you can test the theory against experiments.
The problem was that the math gave a formula for the mass of the proton, but the formula was so complicated nobody could actually solve it, in order to see if its prediction agrees with the proton's true mass. The advance here is to use a supercomputer to solve the formula.
You perhaps could solve it by diagonalizing gigantic matrices, but that's not what they do. The main computational effort comes from computing gigantic multidimensional integrals over millions of variables, one for each point and link in the spacetime lattice. That's what Monte Carlo methods are for; they're the only tractable way to handle very high dimensional integrals.
As noted in other posts, what is exciting about this isn't necessarily that E=mc^2 is confirmed (that's been done plenty of times before), but that it was done in a quantum world (which historically has been at odds with relativity).
What's exciting is, technically, that people were able to calculate the energy of the quark-gluon fields inside a baryon. Everyone knew what it had to be (the difference between the baryon mass and the masses of the quarks inside), but nobody had been able to calculate it directly from theory.
E=mc^2 has never been at odds with quantum field theory. It's only relativistic gravity which is at odds with quantum mechanics.
There is such a thing as relativistic mass, but most people just call it "energy" (or "mass-energy" when they're being pedantic), since as you say, you can't just blindly plug it into all the relativistic formulas where mass appears.
Nobody expected E=mc^2 to be violated. That's not why they ran the calculation. They ran the calculation because, until now, nobody has been able to calculate the mass of a proton from the masses of its constituent quarks. You could write down the formula, but it takes a supercomputer to solve it.
So in this scenario, are they then combining the two types of mass to account for 100%? The type of mass that accounts for 95% of the particle is the energy given off from gluons and quarks, which is a relativistic mass since movements and interactions don't have intrinsic mass? But the intrinsic mass of quarks makes up 5%?
Yeah, that's basically it.
Aren't they confusing various definitions of mass to explain the total mass which they think should be there?
The conserved quantity is relativistic mass. The relativistic mass of the quarks, plus the relativistic mass of the gluons, equals the relativistic mass of the proton.
This is somewhat confused by the fact that relativistic and intrinsic mass of a particle are the same at rest. So if the quarks aren't moving too much, you can basically equate their relativistic mass with their rest mass. I'm not sure which is the 5% they refer to. And then, if the proton is at rest, then the relativistic mass which all the constituents add up to becomes the proton's "intrinsic" mass, treating it as a single particle.
You're right. The "intrinsic" mass is usually called "invariant" mass or sometimes "rest mass" (although the latter doesn't apply to photons). The "relativistic mass" is called "relativistic mass", or "total mass-energy".
Take 'global warmming' both sides have a lot of theory but very little in the way of good tests that can prove it one way or the other.
You can test it by observing that natural sources of warming don't agree with the magnitude, rate, or timing of the observed warming; and that human sources do. You can further observe, for instance, that an enhanced greenhouse effect will lead to stratospheric cooling as a result of heat being trapped lower in the troposphere, and we do observe that. There are further predictions which distinguish manmade warming from various types of natural warming, depending on the type of natural warming. For instance, warming from the atmosphere means the oceans warm from the top down, which is observed, and disagrees with theories that have the surface heat come from the oceans. The greenhouse effect also means that you get shifts in the diurnal and seasonal patterns of warming which disagree with the shifts predicted by solar-induced warming, because of the daily/seasonal patterns in sunlight shifts which do not occur for the greenhouse effect. And so on.
No. They're just verifying that gluons contribute to the binding energy of baryons. A gravitational analogy: we know that the total energy of a binary star system is different from the energy of two random stars millions of light years away from each other. That's because the energy of the system is not just the mass of the stars, but the star masses plus the gravitational energy in the system. For protons, the quarks are like individual stars. We knew that the mass of the proton equals the mass of the quarks plus their binding energy (from the strong force), but until now, we weren't able to calculate that energy.
This doesn't have relevance to dark matter because dark matter can't be due to nuclear binding energy between distant particles: the nuclear force is short ranged.
It's not solving the Dirac equation (which is for a free fermion), but the full Yang-Mills equations, including the strong nuclear force. And they're not really solving DEs by finite element methods. They're evaluating functional integrals via Monte Carlo (integrating configurations over field space). But the functional to be evaluated (the action) is defined on a spacetime lattice and involves field derivatives, which is where the finite differencing comes in.
Science can't tell you whether some theoretical construct is "really" there. That's a matter of philosophical definition. All science can tell you is whether the predictions of theories agree with what is observed in the world.
Although the point of the exercise wasn't actually to verify E=mc^2, it was to develop a computer simulation capable of calculating the masses of baryons using quantum chromodynamics. You could write down a formula for them, but nobody had been able to solve it.
Most areas of science strongly rely on philosophy, and most scientists understand it poorly, usually to the detriment of the technical quality of their work.
What a foolishly over-general remark.
Fine, there are scientists who are armchair philosophers in their spare time. But the vast majority of published scientific work does not intersect with philosophy in any way that meaningfully impacts its technical quality. Hardly anyone publishes papers whose technical content involves, say, free will, or any other serious philosophical issue. If you're want to include "the scientific method", you have to provide evidence that scientists' philosophical misunderstandings of their own methods usually have a detrimental impact on their technical work. A few cherry-picked anecdotes of particularly philosophical work doesn't count.
If you disagree, please go to, say, the last issue of Physical Review Letters and enumerate the papers for which the authors' poor understanding of philosophy had a significantly detrimental impact on the technical quality of the paper.
You could try the two-volume Bamberg and Sternberg, A Course in Mathematics for Students of Physics. I think it could conversely work as a course in physics for students of mathematics. And Arnold, Mathematical Methods of Classical Mechanics. Or Nayfeh and Balachandran, Applied Nonlinear Dynamics Also Lawrie, A Unified Grand Tour of Theoretical Physics. Terse and gives you the equations up front.
If you're into differential geometry you could try The Geometry of Physics by Frankel, or Schutz's Geometrical Methods of Mathematical Physics. But that's pretty advanced physics, general relativity, gauge theory, quantum field theory and such.